Consider an experiment that consists of selecting a card at random from an ordinary deck of cards. Let the random variable X equal the value of the selected card, where Ace = 1, Jack = 11, Queen = 12, and King = 13. Thus, the space of X is S = {1, 2, 3, . . . , 13}. If the experiment is performed in an unbiased manner, assign probabilities to these 13 outcomes and compute the mean μ of this probability distribution.

Step 1 of 3:

The experiment given is selection of card at random from a deck of cards.

Let the random variable X be the value on the selected card,where the value of Ace=1,Jack=11,Queen=12 and King=13.

Therefore the sample space of X becomes,S={1,2,3,4,5,6,7,8,9,10,11,12,13}

Step 2 of 3:

The experiment is an unbiased experiment. That is all the outcomes in the sample space has an equal probability of being selected.

The total number of cards in a deck of cards is n=52. The total number of Aces is 4,total number of Jacks is 4, total number of Kings is 4 and total number of queens is 4 in a total of 52 cards.

The favourable number of outcomes for these 13 outcomes,S={1,2,3,4,5,6,7,8,9,1,0,11,12,13} is 4.

Therefore all these 13 outcomes have an equal probability of .

That is P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=P(7)=P(8)=P(8)=P(9)=P(10)=P(11)=P(12)=P(13)=

=

Therefore, the probability of each outcome is .